Aldo Riello

Research Interests

My main research interests are in quantum gravity. Quantum gravity is ultimately the problem of devising a theory of quantum matter which interacts gravitationally. Since our understanding of gravitation is in terms of a dynamical spacetime, quantum gravity is often restated as the problem of finding a quantum theory of spacetime itself. My work focuses on the interface between non-perturbative background independent approaches to quantum gravity, topological quantum field theories, and discrete quantum geometries. In the last year, I focused on various projects.

Together with the faculty member B.Dittrich and her PhD student C. Delcamp, I developed a new representation for non-perturbative 2+1 dimensional quantum gravity, dual to the usual Ashtekar-Lewandowski representation of Loop Quantum Gravity (more specifically, although slightly loosely, it is based on curvature, rather than metric, defects). We used this basis for developing a new approach to the calculation of entanglement entropy. [JHEP 1611 (2016) 102, JHEP 1702 (2017) 061]

In collaboration with H. Gomes, another postdoc at PI, I put forward a proposal for a gauge-invariant form of symplectic geometry in finite spacetime regions; the main tool employed is a connection 1-form in field-space, that can be thought as providing an abstract observer and whose algebraic properties are closely related to the BRST ghosts. [JHEP 1705 (2017) 017]

I also kept working on an older project of mine, that is 4d Loop Quantum Gravity with a cosmological constant. Investigations in this area led me to propose a deformed, completely self-dual, version of the Yang-Mills phase space on a lattice. This deformed, self-dual, phase space, bears interesting relationships with recent work in (3+1)d Topological Quantum Field Theories, in the Hamiltonian framework, by Walker & Wang, and more recently Dittrich [arXiv:1706.07811 hep-th].

Finally, I am finalizing (two papers under reduction, and another one in project) the study of Euclidean 3d Loop Quantum Gravity on a (filled) torus. The interest of this study is comparing the Loop Quantum Gravity non-perturbative results with the 1-loop exact calculations done in the usual QFT framework. Quite remarkably, and via totally different techniques (deeply rooted in the finiteness of the "spacetime" region under study, rather than on an Euclidean path integral on an infinite space and periodic time), the results are perfectly compatible, modulo some interesting non-perturbative corrections. This project is done in collaboration with B. Dittrich (PI), E. Livine (ENS Lyon), and C. Goeller (PI & ENS Lyon), a PhD student I supervised during his master project. [to appear soon]